1. Field of the Invention
This invention relates to optical filters developed through writing volume holographic gratings in photorefractive material and more particularly to recordation of reflection Bragg Gratings used as optical filters.
2. Description of Related Art
Reflection Bragg Gratings are volume gratings that are written by recording volume holograms created by the interference between two optical beams. Writing the volume holograms may be performed through transmission geometry or reflection geometry setups.
FIG. 1A shows a conventional reflection Bragg Grating recording system in transmission geometry and FIG. 1B shows a conventional reflection Bragg Grating recording system in reflection geometry. In transmission geometry, beams of light 1, 2 are incident on one side of a target 3 and the interference pattern of the two beams within the target 3 is recorded. In reflection geometry, beams of light 10, 20 are incident upon opposite sides of a target 30 and their interference pattern is recorded.
As shown in FIG. 1B, when recording the reflection Bragg Grating in reflection geometry, two optical beams 10, 20 are transmitted through opposite faces of a recording medium 30. The recording medium 30 may also be referred to as a target or a sample and it may be made from a material such as lithium niobate or photothermorefractive glass. The interference pattern caused by the two beams 10, 20 intersecting at the center of the recording medium 30 is recorded. Each beam 10, 20 enters the recording medium 30 at the same angle of incidence, interferes with the other beam 20, 10, and continues through the medium 30 to exit from the opposite face. The interference patterns are used to record the volume holograms within the medium 30.
Typical systems for recording Bragg Gratings, in either reflection or transmission geometries, include wavefront-splitting interferometers, phase-masks, or amplitude-splitting interferometers. The wavefront-splitting interferometer systems carve out two interfering beams from different areas of the wavefront of a spatially coherent beam. Such splitting, however, results in diffraction at the boundary of the cut, causing parasitic interference fringes. Further, additional beam expansion is necessary if large-sized gratings are to be recorded.
In phase-mask systems, a phase mask is illuminated by a single laser beam, creating interfering beams on a closely positioned target. Large-sized or thick gratings cannot be recorded with these systems.
In amplitude-splitting interferometer systems, which are the most common, two interfering beams are created by splitting a parent beam in two, and combining the two beams on a target in reflection or transmission geometry. When recording a Bragg Grating in reflection geometry with two counter propagating beams, the grating may only be reconstructed at a wavelength shorter than the wavelength used for recording. However, the spectral region of photosensitivity for holographic material is often smaller than the needed region of grating operation, making recording in reflection geometry difficult. For example, an spectral region of interest for laser and communication applications is 1000-2000 nm, and the photosensitivity regions of materials that are suitable for recording Bragg Gratings, such as lithium niobate and photothermorefractive glass, are 370-700 nm and 280-370 nm, respectively.
When the wavelengths corresponding to the photosensitive regions of the recording material are many times smaller than the wavelengths of interest for the Bragg Grating, the angles of incidence become too small to be practicable for use in reflection geometry. The relationship between the photosensitive wavelengths of the recording media, the wavelengths of interest and the angles of incidence is explained in an example below.
When a reflection Bragg Grating is recorded at a wavelength λIR inside a material that at the wavelength λIR has a refractive index nIR, the period of the grating is equal to λIR/(2nIR). To record such a grating with beams having a short wavelength λUV, the beams must propagate at an angle 2θ with respect to each other in the media with a refractive index nUV. As explained in H. Kogelnik, “Coupled wave theory for thick hologram gratings,” The Bell System Technical Journal, v. 48, pp. 2909-2945, 1969, that is incorporated herein by reference, the angle θ can be found through the following relationship: sin θ=(nIRλUV)/(nUVλIR). If the wavelengths λUV and λIR differ by a factor of 2 to 5, such that λIR is between twice to five times λUV, the angle between the beams 2θ will be less than 60°. This is too small of an angle for irradiation of the target from the lateral sides because under such an angle, the beams traveling in air cannot penetrate into the standard media with refractive indices of about 1.5. Using the spectral region of wavelengths in the range of 1000-2000 nm, and recording material of wavelengths in the range of 280-700 nm, the ratio of λUV/λIR falls in the range 1.4 to 7 that yields angles between the incident beams that are too small to penetrate the recording medium from air.
When reflection Bragg Gratings for longer wavelengths such as those actually used in communication applications are required, using reflection geometry for the recording process becomes impracticable. As a result, these Bragg Gratings are written in transmission geometry while they are read in reflection geometry. However, the technique of writing a Bragg Grating in transmission geometry and reading it in reflection geometry has drawbacks of its own. Accordingly, recording in transmission geometry and reading in reflection geometry is not desirable.
One method for recording in reflection geometry despite the large difference between the wavelengths of the target medium and the desired wavelengths of the transmission medium is use of prisms as shown in FIG. 2A. The recording method shown in FIG. 2A counters the above problems by positioning a recording media, i.e. a target 30, between two prisms 40, 50, that are made of low-absorbing material such as fused silica, and connecting the target 30 to the prisms with a liquid with an index of refraction, or refractive index, similar to the index of refraction of the target. The beams 10, 20 propagate through the prisms 40, 50 without high absorption and reach the target 30 without unnecessary losses. This allows the recording of Bragg Gratings without the need for high quality polishing, and may sufficiently deflect the beams transmitted in the prisms 40, 50 and the target 30 such that the angle 2θ between the beams 10, 20 in the target 30 is equal to the required angle while the beams are still capable of penetrating the target.
Usually, the accuracy of wavelength positioning needed for communication and laser techniques is about 0.1 nm. To achieve this level of accuracy in the wavelength, the angle between the incident beams 10, 20 must be accurately repeatable. The relationship between the accuracy of the wavelength and the accuracy of the angle 2θ between the incident beams is explored below. If, for example, a reflection Bragg Grating is to be recorded at 1550 nm in photothermorefractive glass with a beam at 325 nm, the angle between the recording beams is found from sin θ=(nIRλUV)/(nUVλIR) to be 2θ=0.42 radians, or approximately 24°. In this calculation nIR˜nUV, and the small difference in refractive indices at different wavelengths is neglected. Differentiating this equation, one can find Δθ=−tan θ·(ΔλIR/λIR). Using this equation, if at λIR=1550 nm the accuracy in the wavelength is ΔλIR=0.1 nm, then ΔλIR/λIR=0.1/1550 which yields a Δθ˜1.4×10−5 radians. This means that the angle 2θ between the angles between the beams should be repeatable with an accuracy of Δθ˜1.4×10−5 radians or approximately 3″ (seconds).
FIG. 2B shows the conventional reflection Bragg Grating recording system of FIG. 2A when there is an error in the position of the prisms. Any small error in the position of one or both of the prisms 40, 50 can change the beam directions and lower the reproducibility of the grating spatial frequency. For example, instead of having its intended rectangular cross section with perfectly parallel sides, the plate of the photorefractive glass that is used as the target 30 may have only substantially parallel sides with a deviation from the ideal or intended shape in the form of a wedge of approximately Δα. This is equivalent to having a change of approximately Δα in the angular location of the prism 40 as shown in the dashed line of FIG. 2B. Therefore, the angle α1 of incidence of the beam on the surface of the prism 40, the angle 2θ between the beams 10, 20, and the Bragg Grating frequency will also be changed.
The resultant change in the angle 2θ between the beams can be determined through Snell's Law that applies to a beam propagating from a first medium with a refractive index n1 into a second medium with a refractive index n2. If the angle of incidence of the beam at the boundary between the first and second mediums from a normal to the boundary is α1 then, the angle α2 between the refracted beam in the second medium and normal is calculated from the relationship: n1 sin α1=n2 sin α2. The amount by which the beam is deflected from its original path in the second medium is α1−α2. When the prism constituting the second medium is moved from its original position by an angle Δα, then the angles α1 and α2 will change by Δα1 and Δα2, respectively. The angles may change to α1−Δα1 and α2−Δα2 or to α1+Δα1 and α2+Δα2, but Snell's Law is preserved such that, for example, n1 sin(α1−Δα1)=n2 sin(α2−Δα2). Differentiation of Snell's Law results in the following relationship:Δα1−Δα2=Δα1[1−[(n1 cos α1)/(n2 cos α2)]]  (equation 1)
This equation expresses the relationship of the difference Δα1−Δα2 between the change Δα1, Δα2 in each of the angles of incidence and refraction from the normal at the prism boundary and the original value of the angles α1, α2. After crossing the boundary into the medium with the refractive index n2, the angle of deviation of the beam from its original path in the medium with the refractive index n1 is equal to α1−α2. The change in the angle of incidence Δα1 results in a deviation of the refracted beam Δα2 and in a change of the total beam deviation Δα1−Δα2.
As discussed above, to achieve a reproducibility of 0.1 nm, the change in the angle between the two beams is Δθ˜1.4××10−5 radians. The amount Δθ is equal to Δα1−Δα2. Assuming n1=1 (air), n2=1.5 (glass), α1≈α2≈0, Δα1=Δα, and Δα1−Δα2=1.4×10−5 radians, then it may be calculated from equation 1 that Δα≈4×10−5 radians. The wedge tolerance Δα must therefore be less than 4×10−5 radians or 8″ (seconds) to provide above-mentioned reproducibility of Bragg Grating parameters. This would require special high quality preparation of the target 30 for Bragg Grating recording.